Accelerated Non-Overlapping Domain Decomposition Method for Total Variation Minimization

Accelerated Non-Overlapping Domain Decomposition Method for Total Variation Minimization

Year:    2021

Author:    Zhenwei Zhang, Xue Li, Huibin Chang, Zhenwei Zhang, Yuping Duan, Huibin Chang, Yuping Duan

Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 4 : pp. 1017–1041

Abstract

We concern with fast domain decomposition methods for solving the total variation minimization problems in image processing. By decomposing the image domain into non-overlapping subdomains and interfaces, we consider the primal-dual problem on the interfaces such that the subdomain problems become independent problems and can be solved in parallel. Suppose both the interfaces and subdomain problems are uniformly convex, we can apply the acceleration method to achieve an $\mathcal{O}(1 / n^2)$ convergent domain decomposition algorithm. The convergence analysis is provided as well. Numerical results on image denoising, inpainting, deblurring, and segmentation are provided and comparison results with existing methods are discussed, which not only demonstrate the advantages of our method but also support the theoretical convergence rate.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2020-0146

Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 4 : pp. 1017–1041

Published online:    2021-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:    Non-overlapping domain decomposition method primal-dual algorithm total variation Rudin-Osher-Fatemi model Chan-Vese model.

Author Details

Zhenwei Zhang

Xue Li

Huibin Chang

Zhenwei Zhang

Yuping Duan

Huibin Chang

Yuping Duan